document.write( "Question 1106283: which of the following represents exponential decay?
\n" ); document.write( "1.\"y=3%5E%280.45x%29\"
\n" ); document.write( "2.\"y=1.05%5E%280.35x%29\"
\n" ); document.write( "3.\"y=%281%2F3%29%5E%28-x%29\"
\n" ); document.write( "4.\"y=4%5E%28-1.25x%29\" \n" ); document.write( "
Algebra.Com's Answer #721245 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Exponential decay is always represented by a curve that's\r\n" );
document.write( "going down on the far right, approaching a horizontal line,\r\n" );
document.write( "usually the x-axis. \r\n" );
document.write( "\r\n" );
document.write( "1.\"y=3%5E%280.45x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C3%5E%280.45x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "No, that's going up on the right, so it's not going down \r\n" );
document.write( "approaching a horizontal line on the far right, so it's not \r\n" );
document.write( "decaying.\r\n" );
document.write( "\r\n" );
document.write( "2.\"y=1.05%5E%280.35x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C1.05%5E%280.35x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "No, that's going up on the right very slowly, so it's not \r\n" );
document.write( "going down approaching a horizontal line, so it's not \r\n" );
document.write( "decaying.\r\n" );
document.write( "\r\n" );
document.write( "3.\"y=%281%2F3%29%5E%28-x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%281%2F3%29%5E%28-x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "No, that's going up on the right, so it's not going down \r\n" );
document.write( "approaching a horizontal line, so it's not decaying.\r\n" );
document.write( "\r\n" );
document.write( "4.\"y=4%5E%28-1.25x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%284%29%5E%28-1.25x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Yup, that's going down approaching the x-axis,\r\n" );
document.write( "so it's the only one decaying.\r\n" );
document.write( "\r\n" );
document.write( "The rule is this. If its equation is of the form:\r\n" );
document.write( "\r\n" );
document.write( "\"y=a%5E%28bx%29%29\", where a is positive and not 1, and\r\n" );
document.write( "b is not 0.\r\n" );
document.write( "\r\n" );
document.write( "then \r\n" );
document.write( "\r\n" );
document.write( "if a > 1, then b < 0 (b must be negative) in order to have \r\n" );
document.write( "exponential decay (approaching the x-axis on the right from \r\n" );
document.write( "above).\r\n" );
document.write( "\r\n" );
document.write( "if a < 1, then b > 0 (b must be positive) in order to have \r\n" );
document.write( "exponential decay (approaching the x-axis on the right from \r\n" );
document.write( "above).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );